The function `f(x)=1+x(sinx)[cosx], 0ltxlepi//2`, where `[.]` denotes greatest integer function

Options

A. is discontinuous is `(0,pi//2)`
B. is strictly decreasing in `(0,pi//2)`
C. is strictly increasing in `(0,pi//2)`
D. has global maximum value 1

Answer

D

Explanation

For `0gtxlepi//2,[cosx]=0` Hence `f(x)=1` for all `xepsilon(0,pi//2)`.
`f(x)` is continuous on `(0,pi//2)`. This function is neither strictly increasing nor strictly decreasing and its global maximum is 1.